Invariant Measures in Coupled KPZ Equations
Invariant Measures in Coupled KPZ Equations
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DOI：
10.1007/978-3-030-15096-9_20
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发表时间：
2017-06
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影响因子：
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通讯作者：
T. Funaki
中科院分区：
文献类型：
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作者：
T. Funaki
讨论了耦合KPZ（Kardar-Parisi-Zhang）方程。其动机来自于对非线性脉动流体动力学的研究，参见。[11，12]。首先简要介绍Funaki和Hoshino [6]的结果，特别是两个近似方程，耦合常数的三线性条件（T），不变测度和解的整体存在性。然后，我们在启发式水平上研究了三线性条件（T）的作用，鉴于不变的措施和重正化的四阶条款。Ertagh和Kardar [2]给出了一个不满足（T）但有不变测度的例子。最后，我们讨论了交叉扩散的情况。
We discuss coupled KPZ (Kardar-Parisi-Zhang) equations. The motivation comes from the study of nonlinear fluctuating hydrodynamics, cf. [11, 12]. We first give a quick overview of results of Funaki and Hoshino [6], in particular, two approximating equations, trilinear condition (T) for coupling constants, invariant measures and global-in-time existence of solutions. Then, we study at heuristic level the role of the trilinear condition (T) in view of invariant measures and renormalizations for 4th order terms. Ertaş and Kardar [2] gave an example which does not satisfy (T) but has an invariant measure. We finally discuss the cross-diffusion case.